I'm talking well beyond my competency, but short of one of those T-cells spontaneously becoming cancerous itself, I don't see how. T-cells do not duplicate them

I'm talking well beyond my competency, but short of one of those T-cells spontaneously becoming cancerous itself, I don't see how. T-cells do not duplicate themselves. Instead, new T-cells are creates in bone marrow. Since they are not editing the genes in the bone marrow, there is no mechanism within the body to create new cells using the modified DNA.